Bayesian Analysis

Given the complexity of the NMR spectra plus restriction on signal-to-noise in both 2H and 13C NMR experiments, an operator- independent spectral analysis would be desirable. It is also important to establish a method which allows a measure of the uncertainties in the metabolic parameters of interest from a single NMR measurement. Bayesian inference coupled with Markov Chain Monte Carlo methods has been developed in collaboration with Dr. Larry Bretthorst at Washington University in St. Louis.

The automated analysis of the 2H free induction decay takes advantage of prior metabolic knowledge (the combined contribution of the TCA cycle, glycogen and glycerol to plasma glucose cannot be greater than 100%) and prior NMR knowledge (chemical shifts) to provide an operator-independent estimate of both the metabolic results and the error in each metabolic parameter from a single raw free induction decay. This analysis is now available for routine use at the Center.

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Analysis of deuterium MAG spectra. 2H NMR spectra from patients with stage 1 (upper) and stage 4 (lower) fibrosis from which the probabilities that glycogen, glycerol or precursors of phosphoenolpyruvate (PEP) contributed to glucose were determined using Bayesian Analysis. Gluconeogenesis from PEP was favored over glycogenolysis in stage 4. For each set of spectral plots in the first column, the bottom graph shows the experimental spectrum, the middle line the spectrum synthesized from optimal parameter estimates, and the upper line is the difference between the two (residuals). The other charts show the probabilities of the fractional contribution of the three substrates to glucose production.

The analysis of 13C free induction decays is also being developed, in which the prior knowledge used includes the relationship between peak intensities and the parameters of models of the citric acid cycle and related pathways.

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Influence of signal-to-noise (S:N) on parameter estimates. NMR spectrum from a heart perfused with [2-13C] acetate was analyzed as obtained (top row, S:N=73) or after adding noise causing a deterioration in S:N to 16 (middle row) or 5 (bottom row). The second two columns show the percent utilization of acetate (Oxidation) and rate of anaplerosis relative to the citric acid cycle flux (indexed at 100%). The numbers in each chart show the optimal estimated model parameter value, and the graphs give the parameter probabilities. Even with an S:N of only 15, the procedure is able to estimate model parameters reliably.